Impact ionization and hot-electron injection derived consistently from Boltzmann transport

We develop a quantitative model of the impact-ionization and hot-electron-injection processes in MOS devices from first principles. We begin by modeling hot-electron transport in the drain-to-channel depletion region using the spatially varying Boltzmann transport equation, and we analytically find a self consistent distribution function in a two step process. From the electron distribution function, we calculate the probabilities of impact ionization and hot-electron injection as functions of channel current, drain voltage, and floating-gate voltage. We compare our analytical model results to measurements in long-channel devices. The model simultaneously fits both the hot-electron-injection and impact-ionization data. These analytical results yield an energy-dependent impact-ionization collision rate that is consistent with numerically calculated collision rates reported in the literature.